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A174784 Expansion of x*(1-x+x^3+x^4)/(1+x^6) (Period 12). 1
0, 1, -1, 0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 1, -1, 0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 1, -1, 0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 1, -1, 0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 1, -1, 0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 1, -1, 0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 1, -1, 0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 1, -1, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Hankel transform of A174783 is -a(n).

LINKS

Table of n, a(n) for n=0..90.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,-1).

FORMULA

a(n) = -cos(5*Pi*n/6)/3 + sin(5*Pi*n/6)/3 - cos(Pi*n/6)/3 + sin(Pi*n/6)/3 + 2*cos(Pi*n/2)/3 + 2*sin(Pi*n/2)/3.

a(n)=(1/12)*{-(n mod 12)+[(n+2) mod 12]+[(n+3) mod 12]-2*[(n+4) mod 12]+[(n+5) mod 12]+[(n+6) mod 12]-[(n+8) mod 12]-[(n+9) mod 12]+2*[(n+10) mod 12]-[(n+11) mod 12]}, with n>=0. - Paolo P. Lava, May 04 2010

G.f.: x*(1-x+x^3+x^4) / ( (1+x^2)*(x^4-x^2+1) ). - R. J. Mathar, Feb 10 2015

MATHEMATICA

LinearRecurrence[{0, 0, 0, 0, 0, -1}, {0, 1, -1, 0, 1, 1}, 100] (* or *) PadRight[ {}, 120, {0, 1, -1, 0, 1, 1, 0, -1, 1, 0, -1, -1}] (* Harvey P. Dale, Feb 25 2017 *)

CROSSREFS

Sequence in context: A284792 A094217 A280261 * A092220 A011655 A102283

Adjacent sequences:  A174781 A174782 A174783 * A174785 A174786 A174787

KEYWORD

easy,sign

AUTHOR

Paul Barry, Mar 29 2010

STATUS

approved

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Last modified November 12 07:03 EST 2019. Contains 329052 sequences. (Running on oeis4.)